Matrix Completion

Matrix completion studies how to recover unobserved entries from partial data, often assuming that rows and columns share a small number of latent factors. It supports tasks such as recommendations, causal-effect estimation from panel data, scientific measurements, and filling gaps in model evaluations. Common approaches include nuclear-norm regularization, low-rank factorization with gradient or Riemannian optimization, and methods that incorporate side information, graphs, or Bayesian models; newer work also explores deep and transformer-based models. A central challenge is balancing sample efficiency and scalability with reliable recovery under noise, structured missingness, heterogeneous groups, and imperfect assumptions about rank or auxiliary information.